Disabled people are likely to be living on lower incomes because of the costs of being disabled and the result of discrimination in the workplace. So it is no surprise they are being hit disproportionately hard by benefit cuts.

Two-thirds of the tenants of Habinteg housing association, which specialises in accessible housing, that are affected by the bedroom tax are disabled. Our research has shown that six months after the new policy was put in place only one-third of them had been exempted from payment by local authorities. The prime minister was mistaken in saying that disabled people have been exempted. This is what should happen, but it's far from the case at the moment.

Ministers defending the policy say people with disabilities should apply for discretionary housing payments – councils' crisis funds for those struggling with housing costs – but know full well that this small pot of money will not come close to meeting demand. Widely differing policies between local councils have created a new postcode lottery across the country with disabled people regularly refused these crisis funds. Three of the four tenants featured in our case studies were refused.

There is more to come, too. When universal credit is introduced disabled people will find the service charges on their home adaptations are no longer reimbursed, and many of those receiving the disability living allowance will lose essential income when they are assessed for the new personal independence payments (Pip).

Only 15% of Habinteg's disabled tenants in general needs properties who receive the disability living allowance, have been exempted from the bedroom tax. Unless many more people are made exempt, the impact of further cuts in disability benefits will be severe for this group.

Independent living is a right and not a privilege – although you wouldn't think so from the direction of government welfare policies. Disabled people should have the same right to independent living as non-disabled people. Government policy supports this in theory, yet benefit cuts are undermining it in practice. Given the chronic shortage of accessible homes, a disabled person told to downsize doesn't even have the very limited options open to others.

Most Habinteg disabled tenants have waited many years for a suitable accessible property. Many have had personalised adaptations made which they would lose if they did move out. Unsurprisingly tenants are mostly trying to stay and pay in order to keep their existing property. Yet faced with the accumulating impact of benefit cuts, paying their rent and maintaining independence and mobility will become harder and harder. It is no exaggeration to say that some may be confronted with an unwanted move to an institutional care setting.

The government needs to acknowledge, understand and act upon the cumulative impact of its welfare reform policies on disabled people, and ensure the rights of all to independence and inclusion. They should repeal the bedroom tax for disabled people, rethink their stance on benefits to cover the upkeep of essential aids and adaptations and revise their plans to cut benefit payments under personal independence payments.

Left unchecked and unchallenged, the welfare reform agenda will create a less inclusive, socially impoverished society of which we will not be proud.